In the Vigornii alphabet there are consonants and vowels. How many different arrangements of letters can be made if exactly vowels must be used and no repetition of letters is allowed?Source: NCTM Mathematics Teacher, February 2006

SOLUTION
1. Choose places out of places to put the vowels
2. Put vowels out of vowels in the chosen places
3. In the remaining places put consonants out of consonants
There are different arrangements.

Answer: 40320Alternative solution1. Choose vowels out of vowels
2. Choose consonants out of consonants
3. How many ways can we form a word with vowels and consonants?
4. For each of the five-letter words how many different ways can we arrange the letters?